Question

How do I solve this system of linear equation using the substitution method?

1/2x- 2/3y= -1
3/7x + y= 18

Answer 1

on the second equation, transpose first the X
Y should remain on the left side

Answer 2

then you have now the value for Y,

try substituting the value of Y on your second equation to the first equation

Answer 3

Any ideas on how to clear the fraction?

Answer 4

multiply both side by the LCD

the LCD is 6, right?

Answer 5

that will give you 3x-4y=-6

Answer 6

on the second equation, multiply both sides by 7, to remove the fraction

Answer 7

the new equation is
3x-4y=-6
3x+7y=126

Answer 8

Yup. So I reworked the problem with the tips that you gave.
3x -4(126-3)= -6
3x-504+12= -6
3x-492= -6
3x=486
x= 162

3(162) - 4y= -6
486- 4y= -6
-4y= -492
y=123

3(162)- 4(123)= -6
-6=-6

Answer 9

alright so you've got it right

based on my computations
x=-182/11
y= -120/11

Answer 10

Thanks!

Answer 11

okay, no problem, you are welcome!

Answer 12

x=14
y=12

Answer 13

@hamidx19 did I work the problem corruptly?

Answer 14

1/2x- 2/3y= -1
3/7x + y= 18

equation 1 divided by -2/3:
y=3/2+3/4x
subbing into eq2:
3/7x+3/4x+3/2=18
33/28x=16.5
x=16.5/(33/28)=14
subbing back into eq1:
7-2/3y=-1, 2/3y=8, y=12

Answer 15

many values of x and y can satisfy the equation!

Answer 16

if your solution satisfies both(all) the given equations then and only then your solution exists.